The problem is your Javascript part:
$(this).siblings().removeClass("active");
You want to access the child elements of the lists. $(this) is the anchor tag you click on and therefor there are no siblings inside this li element.
Try this:
$(this).parent().siblings().each(function () {
$(this).children().removeClass("active");
});
})
This gets the parent list element and is afterwards iterating through the other li's child-elements to remove the active class.
I pasted your code in a JSFiddle - it is pretty ugly and not styled properly but you can see the javascript works.
Edit: The problem with your 90° is that you apply the CSS transition to your li element. Thats why on hover your li element is rotating and on click the anchor inside the li is rotating as well.
A better approach to mine is to put the active class on the list element so you dont have to change anything on the css since the click will prevent the hover from working.
See here: Updated fiddle
$(document).ready(function () {
$(".nav li").click(function () {
$(this).toggleClass("active");
$(this).siblings().removeClass("active");
})
});